DrDelMath
Math 160C College Algebra
Summer 2008
Review Guide for Tests bbbbb
Website: http://www.drdelmath.com
e-mail: del@delweg.com
When sending an e-mail, the subject should be the course name: College
Algebra
TEST 1 : 18 & 19 JUN: Topics to be covered on Test 1 include anything from the text, from the
lectures, from the website, and from the handouts related to the following sections of the textbook.
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Chapter P : Prerequisites
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Section 1.1: Basic Equations
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Section 1.3: Quadratic Equations
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Section 1.5: Other Types of Equations
Section 1.2: Modeling with Equations
Section 1.4: Complex Numbers
o
Equations Involving Radicals
o
Rational Equations

Section 1.6 Inequalities
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Section 1.7: Solving Equations Involving Absolute Value
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Section 2.1: Coordinate Plane
o
Distance Formula
o
Midpoint Formula
Section 2.2: Graphs of Equations in Two Variables
o
Understand Definition of Graph
o
Intercepts
o
Equations of Circles
Section 2.4: Graphs of Linear Equations in Two Variables
o
Standard Form
o
Slope-Intercept Form
o
Point-Slope Form
o
Graphing when given the equation
o
Finding the equation when given conditions
o
Formula for Slope

Section 2.4A: Graphs of Quadratic Equations in Two Variables
o
Intercepts
o
Vertex
o
Shape and Orientation
o
Discriminant
The following essays from Special Topics on the website are included.

Introduction to Sets
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Sets of Numbers
Linear Equations
Quadratics
Finally, if I have failed to list some topic included in the listed sections of the text or essays or
that were included in lectures or on the website they are hereby included in this test.
In short, the test covers everything assigned, discussed or referred to since the beginning of the
class.
TEST 2 : 7 & 8 JUL: Topics to be covered on Test 2 include anything from the text, from the
lectures, from the website, and from the handouts related to the following sections of the textbook.

Section 3.1: Definition of Function
o
o
o
o
o
o

Function Notation
Domain
Range
Rule
Arrow Diagrams
Section 3.2
o
o
o
o
o
o

Definition of Function
Graphs of Functions
Definition of Graph of a Function
Definition of Zero of a Function
Coordinates of Points on the Graph
Determine if a point is on a graph
Arrow Diagrams
Vertical Line Test
Section 3.2A Library of Basic Functions
o
The First Nine Entries and The Absolute Value Function
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Zero Function
Constant Function
Linear Function
Identity Function
Squaring Function
Cubing Function
Quadratic Function
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o
Graph
Shape and Orientation
Discriminant
Sum, Difference, Product, Quotient of functions
Composition of functions
Factoring with respect to composition
Definition
Notation
Horizontal Line test
Finding the Inverse
Show that two functions are inverses
Show that two functions are not inverses
Definition and Elementary Properties
Equivalent Statements about Polynomials
Multiplicities of Zeros
Intermediate Value Theorem
Section 4.2: Dividing Polynomials
The Division Algorithm for Polynomials
The Long Division Process for Polynomials
Remainder and Factor Theorems
Section 4.3: Real Zeros of Polynomial Functions
o
Rational Zeros Theorem
Section 4.4: Complex Zeros and The Fundamental Theorem of Algebra
o
o

Vertex
Section 4.1: Polynomial Functions and their Graphs
o
o
o

Intercepts
Section 3.7: Inverses of Functions
o
o
o
o

General Form
Section 3.6: Combining Functions
o
o
o
o
o
o
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Horizontal Shift
Definition
o
o
o
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Vertical Shift
o
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Absolute Value Function
Section 3.5: Quadratic Functions
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Cube Root Function
Section 3.4 Transformations of Functions
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Square Root Function
Fundamental Theorem of Algebra
Facts about Complex Zeros of Polynomial Functions
Section 4.5: Rational Functions
o
o
o
o
o
Definition, Domain, and Zeros
Vertical Asymptote
Horizontal Asymptote
Important Facts about Rational Functions
Sketching the Graph
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
The following essays from Special Topics on the Web Site are included
o Introduction to Functions
o Linear Functions
o Quadratic Functions
Of course it is presumed that you know all previous material which includes but is not
restricted to:


Definitions

Sets of Numbers
Sets, Set terminology, Set notations, Set Union, Set Intersection
o
o
o
o

Natural, Whole, Integers, Rational, Irrational, Real, Complex
Intervals and Rays
Primes and Composites
Even and Odd Integers
Working with Equations
o
Working with Equations may be helpful
Finally, if I have failed to list some topic included in the listed sections of the text or essays on
the website they are hereby included in this test.
TEST 3 : 21 JUL: Topics to be covered on Test 3 include anything from the text, from the lectures,
from the website, and from the handouts related to the following sections of the textbook.

Section 5.1: Exponential Functions
o
Exponential Function Base e
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
o
Domain, Range, Graph, and it has an inverse
The exponential function base 10 is named exp2 and its rule is exp2 (x) = 2x
Domain, Range, Graph, and it has an inverse
Exponential Function Base a
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The exponential function base 10 is named exp10 and its rule is exp10 (x) = 10x
Exponential Function Base 2
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
o
Domain, Range, Graph, and it has an inverse
Exponential Function Base 10
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
o
The exponential function base e is named exp and its rule is exp(x) = ex
The exponential function base a is named expa and its rule is expa (x) = ax
Domain, Range, Graph, and it has an inverse
Section 5.2: Logarithmic Functions
o
o
o
o
o
ln is the inverse of exp
log is the inverse of exp10
log2 is the inverse of exp2
loga is the inverse of expa
Properties of Natural Logarithm
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
o
ln(1) = 0
ln(e)=1
Properties of Napierian (or Common) Logarithms
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Write an exponential statement as an equivalent logarithmic statement
Write an logarithmic statement as an equivalent exponential statement
Solving Exponential Equations
Solving Logarithmic Equations
Basic definitions as presented on the website
Substitution method
Graphical interpretation of solution of a system of equations
Substitution Method
Gaussian Elimination
Gauss-Jordan Elimination
Matrix methods
Section 6.4 Systems of Inequalities
o
o

Change of base formula
Section 6.3 Systems of Linear Equations in Several Variables
o
o
o
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Log of a power
Section 6.2 Systems of Linear Equations in Two Variables
o
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Log of a quotient
Section 6.1 Systems of Equations
o
o
o
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Log of a product
Section 5.4: Exponential and Logarithmic Equations
o
o
o
o

Boundary line
Graphing
Section 7.1 Matrices and Systems of Equations
o
o
o
o
All the basic definitions related to matrices
The augmented matrix for a system of equations
Elementary Row Operations
Gaussian Elimination and Gauss-Jordan Elimination
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
For this topic the names are less important than the techniques
Section 7.2 The Algebra of Matrices
o
o
o

log(10)=1
Section 5.3: Laws of Logarithms
o
o
o
o

log(1) = 0
Equality, Addition, Opposite, Subtraction, Scalar Multiplication, Multiplication
When Matrix multiplication is defined
Matrix multiplication is not commutative
Section 7.3 Inverses of Matrices and Matrix Equations
o Identity matrix
o Definition of inverse of a matrix
o Elementary Row Operations
o Procedure for finding the inverse of a matrix
o http://www.drdelmath.com/college_algebra/chapter_summaries/matrix_inversio
n.pdf
o
o
o

Solving matrix equations
Matrix equation equivalent to a system of equations
Solving a system of equations using the inverse of the coefficient matrix
Section 7.4 Determinants
o
Definition of determinant
o
o
o
o
o
Determinant as a function
Cofactor
Calculation of the determinant of a 2X2 matrix
Cofactor expansion to calculate the determinant of a 3X3 matrix
det(AB) = det(A)det(B)
Finally, if I have failed to list some topic included in the listed sections of the text or essays on
the website they are hereby included in this test.
COMPREHENSIVE FINAL EXAM: 23 & 24 JUL: Topics to be covered on
COMPREHENSIVE FINAL EXAM include anything from the text, from the lectures, from the website, and from
the handouts related to the sections of the textbook listed above for Test 1, Test 2, and Test 3 as well as
the following sections.

Section 9.1 Sequences and Summation Notation
o
o
o
o
Definition
Traditional as well as function notation
Finding partial sums
Using summation notation
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
Section 9.2 Arithmetic Sequences
o
o
o
o
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For this topic the names are less important than the techniques
Definitions
Arithmetic Sequence as a Linear Function with restricted domain
Determining an arithmetic sequence when given certain facts
Partial Sums
Section 9.6 The Binomial Theorem
o
o
Binomial Coefficients
Expansion of a binomial
Finally, if I have failed to list some topic included in the listed sections of the text or essays on
the website they are hereby included in this test.
Delano P. Wegener, Ph.D.
Instructor
Copyright 2008 by
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